Finite Group Databasebeta

← C2×#13080998 #15632223

Subgroups — C2×#13080998 #15632223

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623061C211yesmaximal, characteristic
2C2×#10623170C211yesmaximal, characteristic, complemented
3#13080998C2116yesmaximal, direct product factor
4C2×#10622491C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622495C211yesmaximal, characteristic, complemented
8C2×#10622412C211yesmaximal, characteristic, complemented
9C2×#10622484C211yesmaximal, characteristic, complemented
10C2×#10622420C211yesmaximal, characteristic, complemented
11C2×#10622661C211yesmaximal, characteristic, complemented
12C2×#10622401C211yesmaximal, characteristic, complemented
13C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
14C2×#10622611C211yesmaximal, characteristic, complemented
15C2×D11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#485C211yesmaximal, characteristic, complemented
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623170—24no—
28#10623170C2218yescomplemented
29#10623061—24no—
30#10623061C2218yes—
31C2×#66948C2211yescharacteristic
32C2×#66946C2211yescharacteristic
33C2×#66945—21no—
34C2×C4⋊C4×D11C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×#66943C2211yescharacteristic
37C2×#66943C2211yescharacteristic
38C2×#66942—21no—
39C2×#66937—21no—
40C2×#66936—21no—
41C2×#66936—21no—
42C2×#66932—21no—
43C2×#66929—21no—
44C2×C4×D44—21no—
45C11×#485C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#106C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66882C2211yescharacteristic
56C2×#66881C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622661C2218yescomplemented
60#10622611C2218yescomplemented
61C2×#66873C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622495C2218yescomplemented
68#10622491C2218yescomplemented
69#10622484C2218yescomplemented
70D11×#106C2218yescomplemented
71#10622422C2218yescomplemented
72#10622420C2218yescomplemented
73#10622412C2218yescomplemented
74#10622401C2218yescomplemented
75#10622350C2218yescomplemented
76(C22⋊D11)⋊C8C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—21no—
80C22×C22⋊D11D411yescharacteristic
81C22×D44—21no—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8C2314yes—
91C11×#117—22no—
92C11×#117C2314yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11D411yescharacteristic
102#66999—22no—
103#66999C2314yes—
104Q8×Dic11—22no—
105Q8×Dic11C2314yes—
106C2×#4325—24no—
107C2×#4325C2314yes—
108#66983—22no—
109#66983C2314yes—
110C4×C22⋊D11D414yes—
111C4×C22⋊D11C2314yes—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4D411yescharacteristic
117#66979—22no—
118#66979C2314yes—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4D411yescharacteristic
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8—24no—
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2314yes—
137C22×C11⋊C8C2311yescharacteristic
138C2×C8×D11—24no—
139C2×C8×D11C2314yes—
140#66948—22no—
141#66948C2314yes—
142#66946—22no—
143#66946C2314yes—
144#66945—28no—
145C4⋊C4×D11—22no—
146C4⋊C4×D11—22no—
147C4⋊C4×D11C2314yes—
148C4⋊C4×D11C2314yes—
149#66943—22no—
150#66943—22no—
151#66943C2314yes—
152#66943C2314yes—
153#66942—28no—
154#66937—28no—
155#66936—28no—
156#66936—28no—
157#66932—28no—
158#66929—28no—
159C4×D44—28no—
160C11×#107C2314yes—
161C11×#106C2314yes—
162C11×#103C2314yes—
163C11×#103C2314yes—
164C11×C22⋊C8C2314yes—
165#66899C2314yes—
166#66885C2314yes—
167#66885C2314yes—
168(C2×D11)⋊C8C2314yes—
169#66882C2314yes—
170#66881C2314yes—
171Dic11⋊C8C2314yes—
172C8×Dic11C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179C2×#3337—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C23×D11—21no—
182C23×D11C2×D411yescharacteristic
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11C2412yes—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—82no—
200C2×C22⋊D11C2×D414yes—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C2×D44—24no—
208C2×D44—21no—
209C2×D44—22no—
210C2×D44—22no—
211C2×D44—44no—
212C2×D44C2412yes—
213C2×C4×D11—24no—
214C2×C4×D11—24no—
215C2×C4×D11—24no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—44no—
219C2×C4×D11—82no—
220C2×C4×D11—82no—
221C2×C4×D11C2×D412yes—
222C2×C4×D11C2412yes—
223C2×C8×C11—22no—
224C2×C8×C11—22no—
225C2×C8×C11C2412yes—
226C2×C8×C11C2412yes—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4C2412yes—
232C11×C4⋊C4C2412yes—
233C11×C4⋊C4C2412yes—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C42×C11—24no—
237C22⋊Dic11—24no—
238C22⋊Dic11C2×D414yes—
239#4325—28no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4C2×D414yes—
245C4⋊Dic11—24no—
246C4⋊Dic11—24no—
247C4⋊Dic11—24no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11C2412yes—
252C4⋊Dic11C2412yes—
253C4⋊Dic11C2412yes—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4C2×D414yes—
260C4×Dic11—24no—
261C4×Dic11—24no—
262C4×Dic11C2×D412yes—
263C4×Dic11C2412yes—
264C2×C11⋊C8—28no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8#4114yes—
267C2×C11⋊C8C2412yes—
268C2×C11⋊C8C2412yes—
269C8×D11—28no—
270C2×#553—111no—
271C2×#552—111no—
272#3337—1116no—
273C2×#499—111no—
274C2×#484—111no—
275C2×#485D1111yescharacteristic, complemented
276C2×#482—111no—
277C2×#480—111no—
278C2×#479—111no—
279C2×#478—111no—
280C2×#465—111no—
281C2×#465—111no—
282C2×C4×SD16—111no—
283C2×C8×D4—111no—
284C2×#427—111no—
285C22×#106—111no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11C22×D412yes—
290C23×C11C22×D411yescharacteristic
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11#13514yes—
298C22×D11C22×D412yes—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—42no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4112yes—
317C2×C4×C112−1+412yes—
318C2×C4×C11C2511yescharacteristic
319C22⋊D11—28no—
320C22⋊D11—84no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11C22×D412yes—
331C2×Dic11C22×D412yes—
332C2×Dic11C22×D412yes—
333D44—22no—
334D44—22no—
335D44—48no—
336D44—42no—
337C4×D11—24no—
338C4×D11—22no—
339C4×D11—22no—
340C4×D11—48no—
341C4×D11—84no—
342C4×D11—84no—
343C8×C11—22no—
344C8×C11—22no—
345C11⋊C8—22no—
346C11⋊C8C2×#4114yes—
347C22×SD16—111no—
348C23×C8—111no—
349C23×C8—111no—
350#553—118no—
351#553—224no—
352#552—118no—
353#552—224no—
354C2×#126—221no—
355C2×#126—221no—
356C2×#125—111no—
357C2×#125—111no—
358C2×#125—221no—
359C2×#123—221no—
360C2×#123—221no—
361C2×C22⋊Q8—111no—
362C2×C22⋊Q8C2×D1111yescharacteristic
363C2×#121—111no—
364C2×#121—111no—
365C2×#121—221no—
366C2×C4×Q8—111no—
367C2×C4×D4—111no—
368C2×C4×D4—111no—
369C2×C4×D4—221no—
370C2×#117—111no—
371C2×#117—221no—
372C2×#117C2×D1111yescharacteristic
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375#499—118no—
376#485C2×D1118yescomplemented
377#484—118no—
378#482—118no—
379#480—118no—
380#479—118no—
381#478—118no—
382#465—118no—
383#465—118no—
384C4×SD16—118no—
385C8×D4—118no—
386#427—118no—
387C2×#107—111no—
388C2×#107—111no—
389C2×#107—111no—
390C2×#107C2×D1111yescharacteristic
391C2×#106—111no—
392C2×#106—111no—
393C2×#106—111no—
394C2×#106—111no—
395C2×#106—118no—
396C2×#106C2×D1111yescharacteristic
397C2×C4⋊C8—111no—
398C2×#103—111no—
399C2×#103C2×D1111yescharacteristic
400C2×#103C2×D1111yescharacteristic
401C2×#102—111no—
402C2×#102—111no—
403C2×#102—111no—
404C2×C22⋊C8—111no—
405C2×C22⋊C8C2×D1111yescharacteristic
406C2×C4×C8—111no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—44no—
411C22×C11#54712yes—
412C22×C11C2×#13512yes—
413C22×C11#57712yes—
414C22×C11C23×D411yescharacteristic
415C2×D11—28no—
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—84no—
422C2×D11C2×#13514yes—
423C4×C11—22no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11#54712yes—
429C4×C11C22×#4111yescharacteristic
430C4×C11C2×2−1+411yescharacteristic
431Dic11—22no—
432Dic11—22no—
433Dic11—22no—
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437C22×Q8C22×D1111yescharacteristic
438C22×D4—111no—
439C22×D4—111no—
440C22×D4—221no—
441C22×D4—221no—
442C23×C4—111no—
443C23×C4—221no—
444C23×C4—221no—
445C23×C4—221no—
446C23×C4C22×D1111yescharacteristic
447C2×SD16—114no—
448C2×SD16—224no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—114no—
452C22×C8—114no—
453C22×C8—224no—
454C22×C8—224no—
455C22×C8C22×D1111yescharacteristic
456C22×C8C22×D1111yescharacteristic
457#126—228no—
458#126—228no—
459#125—114no—
460#125—114no—
461#125—222no—
462#125—222no—
463#125—228no—
464#123—228no—
465#123—228no—
466C22⋊Q8—22no—
467C22⋊Q8—114no—
468C22⋊Q8—222no—
469C22⋊Q8C22×D1114yes—
470#121—114no—
471#121—114no—
472#121—228no—
473#121—222no—
474#121—222no—
475C4×Q8—114no—
476C4×Q8—222no—
477C4×D4—114no—
478C4×D4—114no—
479C4×D4—114no—
480C4×D4—228no—
481C4×D4—222no—
482#117—22no—
483#117—114no—
484#117—228no—
485#117—222no—
486#117C22×D1114yes—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—222no—
495C2×C4⋊C4—222no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C4⋊C4C22×D1111yescharacteristic
506C2×C4⋊C4C22×D1111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—111no—
510C2×C22⋊C4—111no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C42—21no—
517C2×C42—111no—
518C2×C42—221no—
519C2×C42—221no—
520#107—114no—
521#107—114no—
522#107—114no—
523#107C22×D1114yes—
524#106—114no—
525#106—114no—
526#106—114no—
527#106—114no—
528#106C22×D1114yes—
529C4⋊C8—114no—
530#103—114no—
531#103C22×D1114yes—
532#103C22×D1114yes—
533#102—114no—
534#102—114no—
535#102—114no—
536C22⋊C8—114no—
537C22⋊C8C22×D1114yes—
538C4×C8—114no—
539C2×C11—42no—
540C2×C11#333714yescomplemented
541C2×C11C2×#54711yescharacteristic
542C2×C11C22×#13511yescharacteristic
543C2×C11C2×#57711yescharacteristic
544D11—24no—
545D11—82no—
546C24—111no—
547C24—221no—
548C24D4×D1111yescharacteristic
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8C23×D1112yes—
553C2×D4—114no—
554C2×D4—112no—
555C2×D4—224no—
556C2×D4—224no—
557C2×D4—224no—
558C2×D4—221no—
559C2×D4—222no—
560C2×D4—222no—
561C2×D4—444no—
562C2×D4—882no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—111no—
570C22×C4—111no—
571C22×C4—111no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—224no—
575C22×C4—224no—
576C22×C4—224no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—444no—
583C22×C4—882no—
584C22×C4—882no—
585C22×C4D4×D1112yes—
586C22×C4D4×D1111yescharacteristic
587C22×C4C23×D1112yes—
588C22×C4C23×D1111yescharacteristic
589SD16—228no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—114no—
593C2×C8—112no—
594C2×C8—112no—
595C2×C8—228no—
596C2×C8—228no—
597C2×C8—222no—
598C2×C8C23×D1112yes—
599C2×C8C23×D1112yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—114no—
605C4⋊C4—112no—
606C4⋊C4—112no—
607C4⋊C4—112no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4C23×D1112yes—
620C4⋊C4C23×D1112yes—
621C4⋊C4C23×D1112yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—114no—
625C22⋊C4—114no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C42—24no—
632C42—112no—
633C42—112no—
634C42—224no—
635C42—224no—
636C11C2×#333711yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—22no—
640C23—114no—
641C23—112no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23C2×D4×D1112yes—
649C23C2×D4×D1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—228no—
654D4—222no—
655D4—222no—
656D4—448no—
657D4—442no—
658D4—884no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—112no—
672C2×C4—112no—
673C2×C4—112no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—224no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—448no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4—442no—
687C2×C4—884no—
688C2×C4—884no—
689C2×C4C2×D4×D1112yes—
690C2×C4C2×D4×D1111yescharacteristic
691C2×C4#41×D1112yes—
692C2×C4#6704312yes—
693C2×C4C24×D1111yescharacteristic
694C8—22no—
695C8—22no—
696C8—114no—
697C8—222no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—114no—
703C22—228no—
704C22—222no—
705C22—222no—
706C22—442no—
707C22—442no—
708C22—442no—
709C22—884no—
710C22#1062318612yes—
711C22D11×#13512yes—
712C22#1062330912yes—
713C22C22×D4×D1111yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—222no—
720C4—222no—
721C4—222no—
722C4—442no—
723C4—442no—
724C4—442no—
725C4#1062318612yes—
726C4C2×#41×D1111yescharacteristic
727C4C2×#6704311yescharacteristic
728C2—42no—
729C2—224no—
730C2—882no—
731C2#1308099814yesdirect product factor
732C2C2×#1062318611yescharacteristic
733C2C2×D11×#13511yescharacteristic
734C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC2×#10623061C2
hypercenterC2×#485D11
hypocenterC11C2×#3337
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10623170C2semidirect
3. #13080998C2direct (N × H)
4. C2×#10622491C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622495C2semidirect
8. C2×#10622412C2semidirect
9. C2×#10622484C2semidirect
10. C2×#10622420C2semidirect
11. C2×#10622661C2semidirect
12. C2×#10622401C2semidirect
13. C2×(C22⋊D11)⋊C8C2semidirect
14. C2×#10622611C2semidirect
15. C2×D11×#106C2semidirect
16. C2×C11×#485C2semidirect
28. #10623170C22semidirect
45. C11×#485C22semidirect
59. #10622661C22semidirect
60. #10622611C22semidirect
67. #10622495C22semidirect
68. #10622491C22semidirect
69. #10622484C22semidirect
70. D11×#106C22semidirect
71. #10622422C22semidirect
72. #10622420C22semidirect
73. #10622412C22semidirect
74. #10622401C22semidirect
75. #10622350C22semidirect
76. (C22⋊D11)⋊C8C22semidirect
275. C2×#485D11semidirect
376. #485C2×D11semidirect
540. C2×C11#3337semidirect
636. C11C2×#3337semidirect
731. C2#13080998direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106230612
C2×#106231702
#130809982
C2×#106224912
C2×#106224222
C2×#106223502
C2×#106224952
C2×#106224122
C2×#106224842
C2×#106224202
C2×#106226612
C2×#106224012
C2×(C22⋊D11)⋊C82
C2×#106226112
C2×D11×#1062
C2×C11×#4852
C2×#333711